Print all longest common sub-sequences in lexicographical order - GeeksforGeeks

This problem is an extension of longest common subsequence. We first find length of LCS and store all LCS in 2D table using Memoization (or Dynamic Programming). Then we search all characters from ‘a’ to ‘z’ (to output sorted order) in both strings. If a character is found in both strings and current positions of character lead to LCS, we recursively search all occurrences with current LCS length plus 1.

When you calculate a cell in the DP table, keep a backpointer to the previous cell used for that result. If there is a tie, keep multiple backpointers for all of the tied results. Then retrace the path using the backpointers, following all paths.

I can even do this without keeping an extra backpointer. I can use the precalculated DP table to do so. But the problem(to me) occurs when there is a tie

LCS Problem Statement: Given two sequences, find the length of longest subsequence present in both of them. A subsequence is a sequence that appears in the same relative order, but not necessarily contiguous. For example, “abc”, “abg”, “bdf”, “aeg”, ‘”acefg”, .. etc are subsequences of “abcdefg”. So a string of length n has 2^n different possible subsequences.